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Integration problem

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\int(\frac{x}{\sqrt{1-x^{2}}})dx[/tex]

    2. Relevant equations



    3. The attempt at a solution

    My calculator tells me that the answer should be -sqrt(1-x^2) but if I pick u = sqrt(1-x^2), then dx = (sqrt(1-x^2)*du)/x, which leaves me with -integral((sqrt(1-x^2)/u)du), the problem I am having is getting rid of the "ln(u)" in my final answer, any suggestions?
     
  2. jcsd
  3. Feb 11, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    If u^2=1-x^2
    2u du =-2x dx => - u du = x dx

    Now you'd just get

    [tex]\frac{-u}{u} du[/tex]
     
  4. Feb 11, 2009 #3
    ok got it, thank you
     
  5. Feb 11, 2009 #4

    Mark44

    Staff: Mentor

    Another substitution that works is u = 1 - x^2, du = -2xdx.
    The integrand then becomes -(1/2)du/u^(1/2), which is also an easy one to integrate.
     
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